Catalan numbers

Abstract

This dissertation is about Catalan number that can form a sequence of natural numbers. The nth Catalan number is given in the terms of binomial coefficients: Cn = 1/n+1(2n/n) . There are two methods that are used to derive the nth Catalan number are elaborated. The first method is using recurrence relation and the second method is by using the bijective proof. The relation between Catalan number and group theory is explained. The application of Catalan number in group theory is shown. Catalan number is applied in group theory using balanced parentheses. Catalan number is used to see the different ways of groupings. By using Catalan numbers, the numbers can be multiplied in many orders without changing the orders of the numbers. The grouping using Catalan numbers can only be applied to addition and multiplication. In this dissertation also, various Catalan number problems have been researched. This includes nonintersecting chords problem, polygon triangulation, mountain ranges and diagonal avoiding path. The relation between Catalan numbers and group theory is shown by solving these problems.